Terminal Velocity Essay, Research Paper

SC1: Investigating Terminal Velocity

Introduction

When an object falls through a fluid it accelerates until it reaches its terminal velocity. At this speed the forces acting on it are balanced.

My task is to investigate the factors that affect the terminal velocity of a falling object.

Key Factors

? Mass of ball bearing

? Viscosity/density of the fluid

? Surface area of ball bearing

? Texture of the balls surface

? Temperature

I am going to investigate how mass affects the terminal velocity.

Prediction

I think that as the mass of the ball bearing increases so does the weight of the ball bearing, which requires more friction to balance the ball bearing’s weight thus making the terminal velocity increase.

Mathematical Prediction

I think that the mass of a ball bearing is directly proportional to the terminal velocity. This is because if the mass of ball bearing doubles so does the weight of the ball bearing, which requires twice as much friction to balance the ball bearing’s weight, which then doubles the terminal velocity.

Scientific Knowledge

The scientific knowledge to prove my prediction is that as the mass of the ball bearing increases the weight of the ball bearing is increased that requires more friction to balance the ball bearings weight which increases the terminal velocity.

As the ball bearing accelerates the friction acting against the falling ball bearing increases which in turn balances out the forces applied to the ball bearing which reaches the terminal velocity.

Method

The apparatus was set up as shown (in the diagram on the next page)

Two elastic bands were placed on the tube 60 cm (600 mm) apart measured to the nearest 0.1 cm. The first band placed low enough so that the terminal velocity of the ball bearing was reached before the ball bearing reached the band and the second band placed far enough apart so that there would have been a smaller percentage of error. The elastic bands were placed on the tube so that there are markers for the timing to be started and stopped on a fixed point.

A group of ball bearings were massed with an electric balance and an average of the ball bearings were taken. These ball bearings were massed so that an average mass could be calculated for each size of the ball bearings, by dividing the total mass of the ball bearings by the number of ball bearings.

The ball bearing was placed on the fluids surface and let to fall through the fluid.

A stop clock was started when the ball bearing reached the first elastic band and stopped when it reached the second elastic band.

The results were repeated three times for an accurate average time and any “strange results” were repeated to improve accuracy.

The results are shown in a table on the next page.

Diagram

Results

Average mass results

Ball Number of Balls Mass (g) (2dp) Average mass of one ball (g) (2dp)

A 60 1.80 0.03

B 30 3.37 0.11

C 50 22.07 0.44

D 50 44.20 0.88

E 30 61.54 2.05

Terminal Velocity Results

Average mass (g) (2dp) Distance Fallen (cm) (1dp) Time of Fall (s) (1dp) Terminal Velocity (cm/s) (1dp)

Trial 1 Trial 2 Trial 3 Average

0.03 60.0 50.4 48.6 48.9 49.3 1.2

0.11 60.0 22.9 20.6 20.8 21.4 2.8

0.44 60.0 10.3 10.2 10.3 10.3 5.8

0.88 60.0 7.1 7.0 6.5 6.9 8.7

2.05 60 4.8 4.6 4.7 4.7 12.8

Graph

See graph paper.

Conclusion

I have found that my prediction is correct with the fact that as the mass of the ball bearing increases so does the weight of the ball bearing, which requires more friction to balance the ball bearing’s weight thus making the terminal velocity increase.

Therefore the velocity of the ball bearing would increase which is a greater force than the friction required to balance the ball bearing, which accelerates the ball bearing. As the ball bearing accelerates the friction acting against the falling ball bearing increases which in turn balances out the forces applied to the ball bearing thus reaching the terminal velocity of the ball bearing.

My mathematical prediction, which I have found to be incorrect because the terminal velocity can change not only by the change in the mass of the ball bearing but the change of the viscosity of the fluid or the change of the temperature of the fluid and ball bearing. Also the fact that the mass of the ball bearing is not proportional to the terminal velocity because m1 (1.0 g) a value of average mass and its double m2 (2.0 g) have terminal velocity equivalents p1 (9.4 cm/s) and p2 (13.5 cm/s) (p1 for m1 and p2 for m2). P2 not being the double of p1, which means that, the relationship between average mass of a ball bearing and terminal velocity are not directly proportional.

The relationship between mass of the ball bearing and terminal velocity is that the terminal velocity increases in ever decreasing steps, this is because the larger the average mass the greater the friction required to balance out the forces acting on the ball bearing which in turn increases the drag acting on the ball bearing which lowers the terminal velocity.

Evaluation

I did have some anomalous results. This is because the tube was not exactly upright when I took these results the ball bearings drifted exactly downwards and went into the side of the tube apart from getting drag from being near the side of the tube it gained friction from the solid side of the tube. I repeated this result and removed my incorrect result. The ball bearing with the greatest mass had a volume so great that it had drag from the side of the tube because the tube was too narrow for the ball bearing not to get drag off the side of the tube.

All results that are more than 10% out from any group of results would be considered inaccurate and would be repeated. The uncertainties in my results after any repeated results were sufficiently small enough to keep my results reliable.

My results are not accurate enough to get a full curve of best fit because of the drag on the larger ball bearing as mentioned above.

I have found from my graph that another result could have been taken with the mass of the ball bearing between 0.88g and 2.05g.

I propose these improvements: -

? Wider tube for the ball bearing with an average mass of 2.05g

? A longer tube for a smaller percentage of error

? More results taken to increase accuracy

I suggest that more ball bearings with different masses should have had results taken to increase this investigation. Also all the improvements shown above should be taken into account to extend the experiment.

Bibliography

all mine